Question:
The order of the following differential equation is \(\underline{\hspace{2cm}}\). [in integer]
\[
\left(\frac{dy}{dx}\right)^{2} + 5\frac{dy}{dx} + 4y = 5x^{3}
\]
The order of the following differential equation is \(\underline{\hspace{2cm}}\). [in integer]
\[
\left(\frac{dy}{dx}\right)^{2} + 5\frac{dy}{dx} + 4y = 5x^{3}
\]
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The order of a differential equation is determined by the highest derivative present, regardless of powers or nonlinear terms.
Updated On: Jan 13, 2026
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Correct Answer: 1
Solution and Explanation
The highest derivative present in the differential equation is \[ \frac{dy}{dx} \] Even though it appears as \((dy/dx)^2\), the order of a differential equation depends only on the highest order derivative, not on its power. Since the only derivative present is the first derivative, the order is: \[ \boxed{1} \]
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